MATH 1280 Unit 5

Unit 5 deals with two types of discrete random variables, the Binomial and the Poisson, and two types of continuous random variables, the Uniform and the Exponential.

Depending on the context, these types of random variables may serve as theoretical models of the uncertainty associated with the outcome of a measurement.

Give an example, USING YOUR OWN WORDS (NOT TEXT COPIED FROM THE INTERNET), of how either the Poisson or the Exponential distribution could be used to model something in real life (only one example is necessary). You can give an example in an area that interests you (a list of ideas is below). Give a very rough description of the sample space. There is no need to provide data or analyze anything in R.

If you use an idea from another source, please provide a citation in the sentence and reference entry at the end of your post. Include a citation even if you paraphrase from a website. Please do not copy blocks of text from the Internet--try to use your own words.

When forming your answer to this question you may give an example of a situation from your own field of interest for which a random variable, possibly from one of the types that are presented in this unit, can serve as a model. This is just a suggestion; you can really use an example from any area that interests you. Discuss the importance (or lack thereof) of having a theoretical model for the situation. People can use models to predict business conditions, network traffic levels, sales, and number of customers per day, rainfall, temperature, crime rates, or other such things.

This is more of a theoretical discussion, think of it as how you would decide on which distribution is the best for a future study you would do. As always, reply to 3 or 4 of your peers' posts. The reply should have a minimum of 30 words.

SOLUTION:

We own a small guesthouse in the Fourways area of Johannesburg, South Africa that can take a maximum of eighteen (18) people at any given time. Most of the days, we have a confirmation of ten (10) people per night.

Using Poisson distribution, I will show what the probability of having exactly eight (8) people booked at the guesthouse per night against having more than fourteen (14) people booked per night.

> dpois(x=8,lambda=10)

[1] 0.112599

> 1-ppois(q=14,lambda=10)

[1] 0.08345847

The result of the chance of exactly eight (8) people is 11%. [dpois(x=8, lambda=10)]

dpois() is the definite Poisson probability function or "density" and “x” represent the vector of quantiles ("R Probability," n.d.).

The result of the chance of more than fourteen (14) people is 8%. [1 – ppois(q = 14, lambda = 10)]

ppois() is the cumulative distribution function and “q” represent the vector of quantiles ("R Probability," n.d.).

Reference

R Probability. (n.d.). Retrieved from http://www.columbia.edu/~cjd11/charles_dimaggio/DIRE/styled-4/styled-6/code/

Yakir. B (2011). “The sample space and probability of a random variable”. In Introduction to statistical thinking.